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Theorem eqelssd 3120
 Description: Equality deduction from subclass relationship and membership. (Contributed by AV, 21-Aug-2022.)
Hypotheses
Ref Expression
eqelssd.1
eqelssd.2
Assertion
Ref Expression
eqelssd
Distinct variable groups:   ,   ,   ,

Proof of Theorem eqelssd
StepHypRef Expression
1 eqelssd.1 . 2
2 eqelssd.2 . . . 4
32ex 114 . . 3
43ssrdv 3107 . 2
51, 4eqssd 3118 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1332   wcel 1481   wss 3075 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-in 3081  df-ss 3088 This theorem is referenced by:  fiuni  6873  ennnfonelemrn  11966  ennnfonelemdm  11967  unirnblps  12628  unirnbl  12629  dvidlemap  12866  dviaddf  12875  dvimulf  12876  dvcj  12879  dvrecap  12883
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